Optimization and Decision Making
Optimization has been defined as the process of selecting the values of decision variables that minimize or maximize some quantity of interest and it is a key tool in prescriptive analytics. Optimization models are prescriptive because their outcome is a recommendation of what to do.
Examples:
1. Decision variables: unknowns for which the optimization process will find the best values.
3. Constraints: restrictions or limitations that are either related to technical and practical considerations or they're imposed by managerial policies.
Physical constraint à the capacity of a truck (amount shipped cannot exceed the truck capacity)
Managerial constraint à Requiring that 10% of an advertising budget to be spent in YouTube ads is a managerial policy
The process of building an optimization model consists of translating a problem description into mathematical functions that are based on the decision variables. The transportation problem is a classic example of an optimization problem.
In the transportation problem, there is a set of suppliers and a set of customers. For the sake of simplicity, we are going to assume that there is only one type of product that needs to be sent from suppliers to customers. Suppliers have limited quantities of the product to meet the customer demands. There's a cost associated with sending one unit of product from each supplier to each customer.
Example: five suppliers and four customers and therefore, there are 20 transportation processes.
Examples:
- In logistics, an optimization model can recommend where to build a facility, or how to manage inventory or how to route delivery tracks.
- In finance, optimization can be used to find diversified investment portfolios that maximize returns, and limit risks.
1. Decision variables: unknowns for which the optimization process will find the best values.
- quantities to produce of each product
- quantities to ship from one warehouse to a customer
- amount of money to spend in various types of digital ads
3. Constraints: restrictions or limitations that are either related to technical and practical considerations or they're imposed by managerial policies.
Physical constraint à the capacity of a truck (amount shipped cannot exceed the truck capacity)
Managerial constraint à Requiring that 10% of an advertising budget to be spent in YouTube ads is a managerial policy
The process of building an optimization model consists of translating a problem description into mathematical functions that are based on the decision variables. The transportation problem is a classic example of an optimization problem.
In the transportation problem, there is a set of suppliers and a set of customers. For the sake of simplicity, we are going to assume that there is only one type of product that needs to be sent from suppliers to customers. Suppliers have limited quantities of the product to meet the customer demands. There's a cost associated with sending one unit of product from each supplier to each customer.
Example: five suppliers and four customers and therefore, there are 20 transportation processes.
The solution to a transportation problem is feasible if it satisfies all the demands while staying within the capacity limits of its supplier. To know how good this feasible solution is, we measure the quality of the solution. This is done using the objective function. In the transportation problem, the Objective Function is the Total Cost. The objective here will be to minimize the total cost.
An important feature of optimization models is that, often, the same model can be reinterpreted to be used in more than one setting or industry. For instance, rental car companies sometimes find themselves in situations where their inventory of cars is unbalanced. There may be an excess of certain types of cars in some locations and a deficit in others. In terms of the transportation model, the locations with excess cars can be interpreted as supply locations. And the locations with deficits can be interpreted as demand locations. A transportation model can help a rental car company decide how to move cars from one location to another. The cost could reflect not only distance from one location to another, but also the transportation mode that is used to transfer the vehicles, because they could be driven or moved on a truck to preserve the mileage of the car.
An important feature of optimization models is that, often, the same model can be reinterpreted to be used in more than one setting or industry. For instance, rental car companies sometimes find themselves in situations where their inventory of cars is unbalanced. There may be an excess of certain types of cars in some locations and a deficit in others. In terms of the transportation model, the locations with excess cars can be interpreted as supply locations. And the locations with deficits can be interpreted as demand locations. A transportation model can help a rental car company decide how to move cars from one location to another. The cost could reflect not only distance from one location to another, but also the transportation mode that is used to transfer the vehicles, because they could be driven or moved on a truck to preserve the mileage of the car.